A national chain of department stores ranks its 900,000 salespeople by the monetary value of their sales. Lena's sales are at the $13^{\text {th }}$ percentile, Juan's sales are at the $21^{\text {st }}$ percentile.
(a) Which of the following must be true about Lena's and Juan's sales?
The value of Juan's sales were $\$ 800$ more than Lena's.
The value of Lena's sales were $\$ 800$ more than Juan's.
Both Lena and Juan had sales higher in value than the medlan.
Both Lena and Juan had sales lower in value than the median.
(b) Which of the following must be true about Lena's sates?
The value of Lena's sales were about $13 \%$ of the chaln's total.
The value of Lena's sales was in the top half of all of the salespeople.
Lena sold $\$ 1300$ in merchandise.
Lena had sales lower in value than about $87 \%$ of the salespeople.
Explanation
Recheck

Step 1 ：The question is asking for the interpretation of percentiles in the context of sales. The percentile rank of a score is the percentage of scores in its frequency distribution that are equal to or lower than it. In this case, Lena's sales are at the 13th percentile, which means that 13% of the salespeople have sales equal to or lower than Lena. Similarly, Juan's sales are at the 21st percentile, which means that 21% of the salespeople have sales equal to or lower than Juan.

Step 2 ：For part (a), we can't make any assumptions about the difference in the value of Lena's and Juan's sales based on their percentile ranks. We also can't say that both Lena and Juan had sales higher in value than the median because the median is the 50th percentile, and both Lena and Juan are below this percentile. Therefore, the statement that must be true is that both Lena and Juan had sales lower in value than the median.

Step 3 ：For part (b), we can't say that the value of Lena's sales were about 13% of the chain's total because the percentile rank doesn't provide information about the proportion of the total sales. We also can't say that the value of Lena's sales was in the top half of all of the salespeople because Lena is below the 50th percentile. We can't make any assumptions about the exact value of Lena's sales based on her percentile rank. Therefore, the statement that must be true is that Lena had sales lower in value than about 87% of the salespeople.

Step 4 ：Final Answer: \(\boxed{\text{(a) Both Lena and Juan had sales lower in value than the median.}}\)

Step 5 ：Final Answer: \(\boxed{\text{(b) Lena had sales lower in value than about 87% of the salespeople.}}\)